Universe as Doughnut: New Data, New Debate

Published: March 11, 2003

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But in a paper posted on the physics Web site (at arXiv.org/pdf /astro-ph/0302496) late last month, the three cosmologists wrote that it was "difficult not to be intrigued" that their results bore all the earmarks of what are variously called small, compact, finite or periodic universes.

If the universe is finite in one dimension, like a cylinder or a doughnut, Dr. Tegmark said in an interview, there is a limit to the size of clumps that can fit in that direction. They couldn't be bigger than the universe in that direction, just as a guitar string can only play a note so low, depending on its length. So the biggest blobs would have to squish out in a plane in other directions. The way home around the doughnut would be perpendicular to that plane.

Nobody is yet claiming that this is a revolution. The notion of a special direction is on less firm ground than the discovery of a cutoff of large structures. "More detailed work in needed to clarify what's going on," Dr. Tegmark said.

Dr. Martin Rees, a cosmologist at Cambridge University," said he didn't think there was evidence for "anything crazy" in the data.

Even aficionados of finite universes are guarded. Dr. David Spergel, a Princeton cosmologist and Wilkinson satellite team member, called the results "intriguing," but cautioned that they could also be due to chance.

Dr. Hinshaw called the findings of Dr. Tegmark's team "surprisingly robust," but added, "I'm not sure it says something profound about the universe."

Dr. Alexei Starobinski, a theorist at the Landau Institute in Moscow, proposed in 1984 with his mentor, Dr. Yakov B. Zeldovich, that the universe could have been born as a doughnut. Dr. Starobinski emphasized that an infinite universe with ordinary Euclidean geometry was the most natural universe and still favored by theory.

"However, theory is theory, but observations might tell us something different," he said in an e-mail message.

The Science of Shapes

A Compact Universe

Like Mirrored Halls

The new work involves topology, the branch of mathematics that deals with shapes. Topologists are often accused of not knowing the difference between a coffee mug and a doughnut; because each object has one hole, the two can be deformed into each other and are thus topologically equivalent. In a similar vein, a figure 8 and a pair of eyeglass frames are also the same to a topologist. The more holes, the more complicated the topology.

The simplest topology is just the infinite space of the Euclidean geometry taught in high school. But some cosmologists have a hard time calculating how an infinite universe could have appeared in that kind of space. Nature, they contend, might have had an easier time making a small "compact" universe than an infinite one, and they assume Nature would take the easy way out.

"The basic idea is that God's on a budget," said Dr. George Smoot, a physicist at the University of California's Lawrence Berkeley Laboratory and a leader on the COBE team.

The simplest of these compact universes is something called a 3-torus, a doughnut wrapped in three different dimensions. This object is essentially impossible to visualize: it is the equivalent, in a way, of a cube whose opposite sides are somehow glued together. In two dimensions it works just like the Spacewar screen.

Living in such a universe would be like being inside a hall of mirrors, Dr. Tegmark said. Instead of seeing new stars deeper and deeper in space, you see the same things over and over again as light travels out one side of your cube and back in the other.

This mirror game is not limited to cubes and doughnuts. Over the years mathematicians, particularly Dr. William Paul Thurston, now at the University of California at Davis, and Dr. Jeffrey Weeks, an independent mathematician, have speculated about universes composed of various polyhedrons glued together in various ways.

In 1996 the French astronomer Dr. Jean-Pierre Luminet of the Paris Observatory and his colleagues Dr. Roland Lehoucq and Dr. Marc Lachieze-Rey, both of the Center for Astrophysical Studies in Saclay, France, developed a method called "cosmic crystallography," using galaxy statistics to detect and diagnose the repeating periodic patterns that would be created in the sky by light going around and around in differently shaped universe.

Finite or Infinite?

Problems Are Posed

For Favored Theory

Why would the universe want to do this to us? Partly to avoid the difficulties of the infinite, said Dr. Glenn Starkman, an astronomer at the Case Western Reserve University in Cleveland. Besides being difficult to create, an infinite universe is philosophically unattractive. In an infinite volume, he pointed out, anything that can happen will happen.

"Somewhere there are two guys having this same conversation," Dr. Starkman said in a telephone interview, "except that one of them has a purple phone."

Moreover, the idea that dimensions could be curled in loops occurs naturally in theories that try to unite gravity and particle physics, several physicists pointed out. For example, according to string theory, the leading candidate for a theory of everything, the universe actually has 10 dimensions — 9 of space and 1 of time — rather than the 4 we are familiar with. The extra dimensions are curled up into submicroscopic loops, like the threads in an uncut carpet pile, so that we don't notice them in ordinary life.